Trigonometry & Inverse Trigonometry
General
Grade None
Question:
<p>If <span class="math-inline">\(\tan^{-1}x+\tan^{-1}y+\tan^{-1}z=\pi/2\)</span>, then <span class="math-inline">\(xy+yz+zx=\)</span></p>
0
<strong>1</strong>
-1
xyz
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>Sum formula: <span class="math-inline">$\tan(\sum\tan^{-1})=\frac{x+y+z-xyz}{1-(xy+yz+zx)}$</span>. For sum = π/2, denominator = 0: <span class="math-inline">$xy+yz+zx=1$</span>.</p><p><strong>Answer: (2) 1</strong></p><div class="key-concept"><strong>Key Concept:</strong> Sum of tan⁻¹ = π/2 → denominator of addition formula = 0</div></div>
Correct Answer: 2